This means that if we were to start at any point N
and add up the positive terms
after that point in order, then the partial sums would be unbounded above. Likewise
if we added up the negative terms following N
in order then the sequence of partial
sums would be unbounded below.
What happens if the very first term is already greater than a
How do we know that the sum ever reaches values greater than a?
How do we know that the point k1 is ever reached?
It remains to put this all together and show that the partial sums sm
Try to prove this. (The simple
properties of the absolute value function